GATE PI 2024 PYQ

If is a continuous random variable with the probability density function then the value of is __________. (Answer in integer)

If then is __________. (Answer in integer)

In a complex function [equation] is the imaginary unit, and and are real. If is analytic then which of the following equations is/are TRUE?

A vector field is given as , where> and are the unit vectors along the and axes in the Cartesian frame,>respectively. Then the value of; [equation] where is an elemental path taken over an anticlockwi

The values of function at discrete values of are given in the table. The value of , using Trapezoidal rule is ________.(Rounded off to 1 decimal place) x 0 1 2 3 4 y(x) 1 3 6 9 12

In the Taylor series expansion of around , the coefficient of the term is

Seven cards numbered 1 to 7 are placed in a box. After thoroughly mixing all the cards, one card is drawn at random. If it is known that the number on the card drawn is odd, then the probability that

The following differential equation governs the evolution of variable with time , . [equation] Given the initial conditions and at , the value of at is ________. (Rounded off to 3 decimal places)

If is a matrix such that , where is an identity matrix, then which of the following is TRUE?

The sum of the following infinite series is

If '→' denotes increasing order of intensity, then the meaning of the words [sick → infirm → moribund] is analogous to [silly → → daft]. Which one of the given options is appropriate to fill the blank

The probability of a boy or a girl being born is . For a family having only three children, what is the probability of having two girls and one boy?

Which of the following areas is/are supply chain decision(s)?

Three different views of a dice are shown in the figure below. The piece of paper that can be folded to make this dice is

How many 4-digit positive integers divisible by 3 can be formed using only the digits {1, 3, 4, 6, 7}, such that no digit appears more than once in a number?

Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table. Mutual fund A Mutual fund B Mutual fund C Person 1 ₹10,000

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what

In an election, the share of valid votes received by the four candidates A, B, C, and D is represented by the pie chart shown. The total number of votes cast in the election were 1,15,000, out of whic

The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is

Thousands of years ago, some people began dairy farming. This coincided with a number of mutations in a particular gene that resulted in these people developing the ability to digest dairy milk. Based

A metallic cylindrical pressure vessel, used to store compressed air in a plant, has 1 m mean radius and 4 mm wall thickness. The maximum allowable normal and shear stresses in the cylindrical portion

For polymers, match each process with the most suitable application listed.> Process Application P Extrusion 1 Producing complex parts with close tolerance Q Injection molding 2 Producing thermosettin

A uniform cantilever beam of length and flexural rigidity is loaded by a force as shown in the figure. Assuming that the Euler-Bernoulli beam theory is applicable here, the magnitude of the static def

In an air-standard Otto cycle, the pressure and temperature of air just before the compression stroke are 200 kPa and 26.85 C, respectively. The combustion process is assumed to be a constant volume p

A flat belt drive with pulley of cm radius is designed to transmit 6.283 kW power at 600 RPM. In the figure, is the corresponding torque. If the coefficient of static friction between the belt and the

In the iron-carbon equilibrium phase diagram, the temperature and composition of the eutectoid point are and weight carbon, respectively. If a steel specimen with weight carbon is cooled from to the r

A thin copper wire carries electric current and is insulated by putting a sleeve, of>thickness , over it. In steady state conditions, the rate of heat loss from the insulated>wire per unit length is .

An offset slider-crank mechanism is shown in the figure. If the length cm, then the stroke length (in cm) of the slider is __________. (Rounded off to 1 decimal place)

Which one of the following pure metals has the hexagonal close packed (HCP) crystal structure at room temperature?

In the truss shown in the figure, member AC is an inextensible string, other members are rigid, and ABCD is a square with each side of length . The maximum value of force (in kN) for which the truss w

An irrigation pump is used to draw water from a pond. One end of a 5.05 cm diameter hose pipe is connected to the outlet of the pump at 1.02 m below the surface level, and just after the pump, the sta

The following layout of four departments P, Q, R and S is provided as input to CRAFT (Computerized Relative Allocation of Facilities Technique). Which one of the following department pairs cannot be c

Which one of the following THERBLIGS does not advance the progress of the work and can be eliminated by applying the principles of motion economy?

A company purchased two machines, Machine A and Machine B, at the same time. The purchase price, estimated useful life and the estimated salvage value of the two machines are given in the table. Machi

An assembly line consists of three work stations (S1, S2 and S3) in series to assemble a toy. The times required to perform tasks at these stations are 6, 4 and T minutes, respectively. If the efficie

In a time study, the average time taken for packaging a product in a warehouse by a worker with 120% performance rating is observed as 9 minutes. Assuming an allowance of 10% of the standard time, the

If work sampling is carried out using a large number of observations, then the required sample size is estimated using

Match each of the listed defects in deep drawing cup with the corresponding reason in the table. Defect in deep drawing cup Reason P Orange peel on the surface of cup 1 No blank holding force Q Wrinkl

Mild steel plates are welded to make butt joints by arc welding with 85% heat transfer efficiency ignoring other losses. The first weld joint is made by selecting arc voltage of 30 V and current of 18

To create 12 divisions on a disc by using simple indexing and dividing head on a horizontal milling machine, choose the correct option for the rotation of the crank pin.

A blank of 100 mm diameter is to be cut out of a 2 mm thick sheet through blanking operation. If the radial clearance between the punch and die is 6% of the sheet thickness then the diameter (in mm) o

During orthogonal turning, the cutting speed, feed and depth of cut are set as 2 m/s, 0.2 mm/rev and 2 mm, respectively. The specific cutting energy (neglecting the effect of feed force on the total c

Electro-chemical machining is performed on a flat copper workpiece. If the material removal rate is 2 cm /min throughout the process, then the required current (in A) is ________. (Rounded off to 1 de

Match the configurations of the listed 3 degrees-of-freedom industrial robots with the type of joints. Configuration Type of joints P Cartesian 1 One prismatic and two rotary Q Cylindrical 2 Three rot

For a mild steel specimen subjected to uniaxial tensile load, which of the following is/are TRUE?

In a forming operation, the plastic deformation of a steel specimen starts under plane stress condition, where the principal stresses are Mpa and Mpa. If the steel specimen follows von-Mises yield cri

A CNC milling operation is carried out by moving the tool from the point A to point B in anti-clockwise direction to cut a slot of quarter circle with center at C, as shown. The coordinates of the poi

The solidification time of a cube and a cylinder of the same material, produced through the same sand casting process, is found to be equal. Each side of the cube is , and the radius and the length of

In a sand mold, a sprue of height mm is to be provided for maintaining the molten metal flow rate of mm /s. The height of liquid column above the point 2 is kept constant at mm. The cross-sectional ar

Which of the following concepts is not closely inter-related with INTERCHANGEABILITY in the context of product design?

Which among the following is/are TRUE for friction stir welding (FSW) process?

Choose the item(s) which is/are required to make an eccentric hole on a disc, as shown, using a lathe.

In a single pass cold rolling operation, a flat plate is reduced to a thickness of 3 mm. In this operation, two rolls of diameter 400 mm each are rotating in opposite direction at 300 RPM, and the ela

The following data are given in relation to turning operation of a cylindrical workpiece. Diameter of the workpiece = 160 mm, length of the workpiece = 190 mm, cutting velocity = m/min, and tool feed

Five jobs A, B, C, D and E are available at time for processing at a machine, and their processing times are listed. Job A B C D E Processing time (in days) 9 6 4 5 8 If the jobs are processed using t

Which one of the following methods requires the least amount of data for forecasting?

A company orders an item using the classical economic order quantity formula. If the ordering cost per order is increased by 20% and the demand per unit time is also increased by 20%, then the time be

A project has six activities and the precedence relationship among them is shown in the table. Activity Precedent activities A None B None C None D A, B E B, C F A, B The minimum number of dummy activ

In a single server Markovian queuing system, if the customers arrive following the Poisson distribution, then the inter-arrival time follows

Which of the following is NOT an assumption of a linear programming problem?

Consider the following linear programming problem with two decision variables and . There are three constraints involving resources R1, R2 and R3 as indicated. Maximize Subject to R1 R2 R3 , The optim

The pitch of a metric screw thread is calculated from pitch circle diameter measurement through two-wire method. If the thread is single-start with calculated pitch of 1.4 mm then the diameter (in mm)

Which of the following statement(s) is/are TRUE for a given acceptance sampling plan?

A repairable machine operated for 2400 hours in a year and for that year the machine broke down 8 times. The mean time to repair including waiting time is found to be 20 hours for that year. If the me

Which one of the following is not true about Total Productive Maintenance (TPM)?